Properties

Label 405.4.b.f.244.14
Level $405$
Weight $4$
Character 405.244
Analytic conductor $23.896$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + 4069504 x^{2} + 614656\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{12}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.14
Root \(4.07626i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.f.244.3

$q$-expansion

\(f(q)\) \(=\) \(q+4.07626i q^{2} -8.61587 q^{4} +(-10.3994 - 4.10522i) q^{5} +13.3430i q^{7} -2.51043i q^{8} +O(q^{10})\) \(q+4.07626i q^{2} -8.61587 q^{4} +(-10.3994 - 4.10522i) q^{5} +13.3430i q^{7} -2.51043i q^{8} +(16.7339 - 42.3906i) q^{10} -11.5617 q^{11} +40.0796i q^{13} -54.3893 q^{14} -58.6938 q^{16} -93.3392i q^{17} -75.1002 q^{19} +(89.5997 + 35.3700i) q^{20} -47.1284i q^{22} -142.001i q^{23} +(91.2943 + 85.3835i) q^{25} -163.375 q^{26} -114.961i q^{28} -174.047 q^{29} +248.868 q^{31} -259.334i q^{32} +380.475 q^{34} +(54.7758 - 138.758i) q^{35} +82.9086i q^{37} -306.128i q^{38} +(-10.3059 + 26.1069i) q^{40} +449.454 q^{41} -279.850i q^{43} +99.6140 q^{44} +578.831 q^{46} -33.8764i q^{47} +164.966 q^{49} +(-348.045 + 372.139i) q^{50} -345.320i q^{52} -423.321i q^{53} +(120.234 + 47.4633i) q^{55} +33.4966 q^{56} -709.461i q^{58} -615.628 q^{59} -502.608 q^{61} +1014.45i q^{62} +587.563 q^{64} +(164.535 - 416.803i) q^{65} -57.7537i q^{67} +804.198i q^{68} +(565.615 + 223.280i) q^{70} +252.598 q^{71} -823.934i q^{73} -337.957 q^{74} +647.054 q^{76} -154.267i q^{77} +205.565 q^{79} +(610.379 + 240.951i) q^{80} +1832.09i q^{82} +646.559i q^{83} +(-383.178 + 970.670i) q^{85} +1140.74 q^{86} +29.0248i q^{88} -1324.94 q^{89} -534.780 q^{91} +1223.46i q^{92} +138.089 q^{94} +(780.996 + 308.303i) q^{95} -563.768i q^{97} +672.442i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} + 3 q^{5} + O(q^{10}) \) \( 16 q - 54 q^{4} + 3 q^{5} - 10 q^{10} + 90 q^{11} - 102 q^{14} + 146 q^{16} - 4 q^{19} - 6 q^{20} - 71 q^{25} + 468 q^{26} - 516 q^{29} + 38 q^{31} - 212 q^{34} + 267 q^{35} - 44 q^{40} + 576 q^{41} - 1644 q^{44} - 290 q^{46} + 4 q^{49} + 558 q^{50} + 15 q^{55} + 2430 q^{56} - 2202 q^{59} + 20 q^{61} + 322 q^{64} + 339 q^{65} - 636 q^{70} + 2952 q^{71} - 4080 q^{74} - 396 q^{76} + 218 q^{79} - 1266 q^{80} + 704 q^{85} + 6108 q^{86} - 4074 q^{89} - 942 q^{91} + 1078 q^{94} - 1692 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.07626i 1.44117i 0.693364 + 0.720587i \(0.256128\pi\)
−0.693364 + 0.720587i \(0.743872\pi\)
\(3\) 0 0
\(4\) −8.61587 −1.07698
\(5\) −10.3994 4.10522i −0.930149 0.367182i
\(6\) 0 0
\(7\) 13.3430i 0.720452i 0.932865 + 0.360226i \(0.117300\pi\)
−0.932865 + 0.360226i \(0.882700\pi\)
\(8\) 2.51043i 0.110946i
\(9\) 0 0
\(10\) 16.7339 42.3906i 0.529173 1.34051i
\(11\) −11.5617 −0.316907 −0.158454 0.987366i \(-0.550651\pi\)
−0.158454 + 0.987366i \(0.550651\pi\)
\(12\) 0 0
\(13\) 40.0796i 0.855083i 0.903996 + 0.427541i \(0.140620\pi\)
−0.903996 + 0.427541i \(0.859380\pi\)
\(14\) −54.3893 −1.03830
\(15\) 0 0
\(16\) −58.6938 −0.917090
\(17\) 93.3392i 1.33165i −0.746107 0.665826i \(-0.768079\pi\)
0.746107 0.665826i \(-0.231921\pi\)
\(18\) 0 0
\(19\) −75.1002 −0.906799 −0.453399 0.891307i \(-0.649789\pi\)
−0.453399 + 0.891307i \(0.649789\pi\)
\(20\) 89.5997 + 35.3700i 1.00176 + 0.395449i
\(21\) 0 0
\(22\) 47.1284i 0.456719i
\(23\) 142.001i 1.28735i −0.765297 0.643677i \(-0.777408\pi\)
0.765297 0.643677i \(-0.222592\pi\)
\(24\) 0 0
\(25\) 91.2943 + 85.3835i 0.730355 + 0.683068i
\(26\) −163.375 −1.23232
\(27\) 0 0
\(28\) 114.961i 0.775915i
\(29\) −174.047 −1.11447 −0.557237 0.830354i \(-0.688138\pi\)
−0.557237 + 0.830354i \(0.688138\pi\)
\(30\) 0 0
\(31\) 248.868 1.44187 0.720937 0.693001i \(-0.243712\pi\)
0.720937 + 0.693001i \(0.243712\pi\)
\(32\) 259.334i 1.43263i
\(33\) 0 0
\(34\) 380.475 1.91914
\(35\) 54.7758 138.758i 0.264537 0.670128i
\(36\) 0 0
\(37\) 82.9086i 0.368381i 0.982891 + 0.184190i \(0.0589663\pi\)
−0.982891 + 0.184190i \(0.941034\pi\)
\(38\) 306.128i 1.30686i
\(39\) 0 0
\(40\) −10.3059 + 26.1069i −0.0407376 + 0.103197i
\(41\) 449.454 1.71202 0.856011 0.516957i \(-0.172935\pi\)
0.856011 + 0.516957i \(0.172935\pi\)
\(42\) 0 0
\(43\) 279.850i 0.992481i −0.868185 0.496241i \(-0.834713\pi\)
0.868185 0.496241i \(-0.165287\pi\)
\(44\) 99.6140 0.341304
\(45\) 0 0
\(46\) 578.831 1.85530
\(47\) 33.8764i 0.105136i −0.998617 0.0525678i \(-0.983259\pi\)
0.998617 0.0525678i \(-0.0167406\pi\)
\(48\) 0 0
\(49\) 164.966 0.480949
\(50\) −348.045 + 372.139i −0.984420 + 1.05257i
\(51\) 0 0
\(52\) 345.320i 0.920910i
\(53\) 423.321i 1.09712i −0.836110 0.548562i \(-0.815175\pi\)
0.836110 0.548562i \(-0.184825\pi\)
\(54\) 0 0
\(55\) 120.234 + 47.4633i 0.294771 + 0.116363i
\(56\) 33.4966 0.0799316
\(57\) 0 0
\(58\) 709.461i 1.60615i
\(59\) −615.628 −1.35844 −0.679220 0.733935i \(-0.737682\pi\)
−0.679220 + 0.733935i \(0.737682\pi\)
\(60\) 0 0
\(61\) −502.608 −1.05496 −0.527479 0.849568i \(-0.676863\pi\)
−0.527479 + 0.849568i \(0.676863\pi\)
\(62\) 1014.45i 2.07799i
\(63\) 0 0
\(64\) 587.563 1.14758
\(65\) 164.535 416.803i 0.313971 0.795354i
\(66\) 0 0
\(67\) 57.7537i 0.105310i −0.998613 0.0526548i \(-0.983232\pi\)
0.998613 0.0526548i \(-0.0167683\pi\)
\(68\) 804.198i 1.43417i
\(69\) 0 0
\(70\) 565.615 + 223.280i 0.965771 + 0.381244i
\(71\) 252.598 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(72\) 0 0
\(73\) 823.934i 1.32102i −0.750819 0.660508i \(-0.770341\pi\)
0.750819 0.660508i \(-0.229659\pi\)
\(74\) −337.957 −0.530901
\(75\) 0 0
\(76\) 647.054 0.976607
\(77\) 154.267i 0.228317i
\(78\) 0 0
\(79\) 205.565 0.292758 0.146379 0.989229i \(-0.453238\pi\)
0.146379 + 0.989229i \(0.453238\pi\)
\(80\) 610.379 + 240.951i 0.853031 + 0.336739i
\(81\) 0 0
\(82\) 1832.09i 2.46732i
\(83\) 646.559i 0.855049i 0.904004 + 0.427525i \(0.140614\pi\)
−0.904004 + 0.427525i \(0.859386\pi\)
\(84\) 0 0
\(85\) −383.178 + 970.670i −0.488959 + 1.23864i
\(86\) 1140.74 1.43034
\(87\) 0 0
\(88\) 29.0248i 0.0351598i
\(89\) −1324.94 −1.57802 −0.789010 0.614380i \(-0.789406\pi\)
−0.789010 + 0.614380i \(0.789406\pi\)
\(90\) 0 0
\(91\) −534.780 −0.616046
\(92\) 1223.46i 1.38646i
\(93\) 0 0
\(94\) 138.089 0.151519
\(95\) 780.996 + 308.303i 0.843458 + 0.332960i
\(96\) 0 0
\(97\) 563.768i 0.590124i −0.955478 0.295062i \(-0.904660\pi\)
0.955478 0.295062i \(-0.0953403\pi\)
\(98\) 672.442i 0.693132i
\(99\) 0 0
\(100\) −786.580 735.653i −0.786580 0.735653i
\(101\) 311.591 0.306975 0.153487 0.988151i \(-0.450950\pi\)
0.153487 + 0.988151i \(0.450950\pi\)
\(102\) 0 0
\(103\) 81.5226i 0.0779870i −0.999239 0.0389935i \(-0.987585\pi\)
0.999239 0.0389935i \(-0.0124152\pi\)
\(104\) 100.617 0.0948684
\(105\) 0 0
\(106\) 1725.56 1.58115
\(107\) 145.138i 0.131131i −0.997848 0.0655655i \(-0.979115\pi\)
0.997848 0.0655655i \(-0.0208851\pi\)
\(108\) 0 0
\(109\) −326.484 −0.286894 −0.143447 0.989658i \(-0.545819\pi\)
−0.143447 + 0.989658i \(0.545819\pi\)
\(110\) −193.473 + 490.107i −0.167699 + 0.424817i
\(111\) 0 0
\(112\) 783.148i 0.660719i
\(113\) 52.0212i 0.0433074i 0.999766 + 0.0216537i \(0.00689313\pi\)
−0.999766 + 0.0216537i \(0.993107\pi\)
\(114\) 0 0
\(115\) −582.943 + 1476.72i −0.472694 + 1.19743i
\(116\) 1499.57 1.20027
\(117\) 0 0
\(118\) 2509.46i 1.95775i
\(119\) 1245.42 0.959391
\(120\) 0 0
\(121\) −1197.33 −0.899570
\(122\) 2048.76i 1.52038i
\(123\) 0 0
\(124\) −2144.22 −1.55287
\(125\) −598.887 1262.72i −0.428528 0.903528i
\(126\) 0 0
\(127\) 266.008i 0.185862i −0.995673 0.0929309i \(-0.970376\pi\)
0.995673 0.0929309i \(-0.0296236\pi\)
\(128\) 320.383i 0.221235i
\(129\) 0 0
\(130\) 1699.00 + 670.689i 1.14624 + 0.452487i
\(131\) −2542.39 −1.69565 −0.847825 0.530277i \(-0.822088\pi\)
−0.847825 + 0.530277i \(0.822088\pi\)
\(132\) 0 0
\(133\) 1002.06i 0.653305i
\(134\) 235.419 0.151769
\(135\) 0 0
\(136\) −234.322 −0.147742
\(137\) 123.495i 0.0770140i −0.999258 0.0385070i \(-0.987740\pi\)
0.999258 0.0385070i \(-0.0122602\pi\)
\(138\) 0 0
\(139\) −215.123 −0.131270 −0.0656348 0.997844i \(-0.520907\pi\)
−0.0656348 + 0.997844i \(0.520907\pi\)
\(140\) −471.941 + 1195.52i −0.284902 + 0.721716i
\(141\) 0 0
\(142\) 1029.66i 0.608499i
\(143\) 463.388i 0.270982i
\(144\) 0 0
\(145\) 1809.98 + 714.502i 1.03663 + 0.409215i
\(146\) 3358.57 1.90382
\(147\) 0 0
\(148\) 714.329i 0.396740i
\(149\) −221.877 −0.121993 −0.0609963 0.998138i \(-0.519428\pi\)
−0.0609963 + 0.998138i \(0.519428\pi\)
\(150\) 0 0
\(151\) 495.348 0.266959 0.133480 0.991052i \(-0.457385\pi\)
0.133480 + 0.991052i \(0.457385\pi\)
\(152\) 188.534i 0.100606i
\(153\) 0 0
\(154\) 628.832 0.329044
\(155\) −2588.08 1021.66i −1.34116 0.529430i
\(156\) 0 0
\(157\) 2206.41i 1.12160i 0.827952 + 0.560798i \(0.189506\pi\)
−0.827952 + 0.560798i \(0.810494\pi\)
\(158\) 837.935i 0.421915i
\(159\) 0 0
\(160\) −1064.62 + 2696.92i −0.526037 + 1.33256i
\(161\) 1894.71 0.927477
\(162\) 0 0
\(163\) 931.108i 0.447423i 0.974655 + 0.223712i \(0.0718174\pi\)
−0.974655 + 0.223712i \(0.928183\pi\)
\(164\) −3872.44 −1.84382
\(165\) 0 0
\(166\) −2635.54 −1.23227
\(167\) 1724.43i 0.799045i −0.916723 0.399522i \(-0.869176\pi\)
0.916723 0.399522i \(-0.130824\pi\)
\(168\) 0 0
\(169\) 590.628 0.268834
\(170\) −3956.70 1561.93i −1.78509 0.704675i
\(171\) 0 0
\(172\) 2411.15i 1.06889i
\(173\) 2451.99i 1.07758i −0.842440 0.538790i \(-0.818881\pi\)
0.842440 0.538790i \(-0.181119\pi\)
\(174\) 0 0
\(175\) −1139.27 + 1218.14i −0.492118 + 0.526185i
\(176\) 678.599 0.290633
\(177\) 0 0
\(178\) 5400.81i 2.27420i
\(179\) −1051.07 −0.438885 −0.219443 0.975625i \(-0.570424\pi\)
−0.219443 + 0.975625i \(0.570424\pi\)
\(180\) 0 0
\(181\) −2663.06 −1.09361 −0.546805 0.837260i \(-0.684156\pi\)
−0.546805 + 0.837260i \(0.684156\pi\)
\(182\) 2179.90i 0.887829i
\(183\) 0 0
\(184\) −356.483 −0.142827
\(185\) 340.358 862.198i 0.135263 0.342649i
\(186\) 0 0
\(187\) 1079.16i 0.422010i
\(188\) 291.874i 0.113229i
\(189\) 0 0
\(190\) −1256.72 + 3183.54i −0.479854 + 1.21557i
\(191\) −2223.59 −0.842374 −0.421187 0.906974i \(-0.638386\pi\)
−0.421187 + 0.906974i \(0.638386\pi\)
\(192\) 0 0
\(193\) 4850.19i 1.80894i −0.426542 0.904468i \(-0.640268\pi\)
0.426542 0.904468i \(-0.359732\pi\)
\(194\) 2298.06 0.850471
\(195\) 0 0
\(196\) −1421.32 −0.517974
\(197\) 372.662i 0.134777i 0.997727 + 0.0673884i \(0.0214667\pi\)
−0.997727 + 0.0673884i \(0.978533\pi\)
\(198\) 0 0
\(199\) −4996.59 −1.77990 −0.889948 0.456063i \(-0.849259\pi\)
−0.889948 + 0.456063i \(0.849259\pi\)
\(200\) 214.350 229.188i 0.0757840 0.0810303i
\(201\) 0 0
\(202\) 1270.12i 0.442404i
\(203\) 2322.30i 0.802925i
\(204\) 0 0
\(205\) −4674.04 1845.11i −1.59244 0.628624i
\(206\) 332.307 0.112393
\(207\) 0 0
\(208\) 2352.42i 0.784188i
\(209\) 868.286 0.287371
\(210\) 0 0
\(211\) −563.402 −0.183821 −0.0919104 0.995767i \(-0.529297\pi\)
−0.0919104 + 0.995767i \(0.529297\pi\)
\(212\) 3647.28i 1.18158i
\(213\) 0 0
\(214\) 591.619 0.188982
\(215\) −1148.84 + 2910.26i −0.364421 + 0.923155i
\(216\) 0 0
\(217\) 3320.64i 1.03880i
\(218\) 1330.83i 0.413465i
\(219\) 0 0
\(220\) −1035.92 408.937i −0.317464 0.125321i
\(221\) 3741.00 1.13867
\(222\) 0 0
\(223\) 5374.35i 1.61387i 0.590639 + 0.806936i \(0.298876\pi\)
−0.590639 + 0.806936i \(0.701124\pi\)
\(224\) 3460.29 1.03214
\(225\) 0 0
\(226\) −212.052 −0.0624136
\(227\) 1111.67i 0.325040i −0.986705 0.162520i \(-0.948038\pi\)
0.986705 0.162520i \(-0.0519621\pi\)
\(228\) 0 0
\(229\) −2037.75 −0.588027 −0.294013 0.955801i \(-0.594991\pi\)
−0.294013 + 0.955801i \(0.594991\pi\)
\(230\) −6019.48 2376.23i −1.72571 0.681234i
\(231\) 0 0
\(232\) 436.933i 0.123647i
\(233\) 2127.08i 0.598066i −0.954243 0.299033i \(-0.903336\pi\)
0.954243 0.299033i \(-0.0966641\pi\)
\(234\) 0 0
\(235\) −139.070 + 352.293i −0.0386039 + 0.0977918i
\(236\) 5304.17 1.46302
\(237\) 0 0
\(238\) 5076.66i 1.38265i
\(239\) −1982.88 −0.536659 −0.268330 0.963327i \(-0.586472\pi\)
−0.268330 + 0.963327i \(0.586472\pi\)
\(240\) 0 0
\(241\) −4219.68 −1.12786 −0.563929 0.825823i \(-0.690711\pi\)
−0.563929 + 0.825823i \(0.690711\pi\)
\(242\) 4880.61i 1.29644i
\(243\) 0 0
\(244\) 4330.41 1.13617
\(245\) −1715.54 677.220i −0.447354 0.176596i
\(246\) 0 0
\(247\) 3009.99i 0.775388i
\(248\) 624.767i 0.159971i
\(249\) 0 0
\(250\) 5147.17 2441.22i 1.30214 0.617584i
\(251\) 1638.58 0.412057 0.206028 0.978546i \(-0.433946\pi\)
0.206028 + 0.978546i \(0.433946\pi\)
\(252\) 0 0
\(253\) 1641.77i 0.407972i
\(254\) 1084.32 0.267859
\(255\) 0 0
\(256\) 3394.54 0.828745
\(257\) 6167.31i 1.49691i 0.663184 + 0.748456i \(0.269205\pi\)
−0.663184 + 0.748456i \(0.730795\pi\)
\(258\) 0 0
\(259\) −1106.25 −0.265401
\(260\) −1417.62 + 3591.12i −0.338142 + 0.856583i
\(261\) 0 0
\(262\) 10363.5i 2.44373i
\(263\) 6361.88i 1.49160i 0.666171 + 0.745799i \(0.267932\pi\)
−0.666171 + 0.745799i \(0.732068\pi\)
\(264\) 0 0
\(265\) −1737.82 + 4402.27i −0.402844 + 1.02049i
\(266\) 4084.65 0.941526
\(267\) 0 0
\(268\) 497.598i 0.113417i
\(269\) 2404.84 0.545077 0.272539 0.962145i \(-0.412137\pi\)
0.272539 + 0.962145i \(0.412137\pi\)
\(270\) 0 0
\(271\) 6986.46 1.56604 0.783021 0.621995i \(-0.213678\pi\)
0.783021 + 0.621995i \(0.213678\pi\)
\(272\) 5478.43i 1.22125i
\(273\) 0 0
\(274\) 503.398 0.110991
\(275\) −1055.52 987.178i −0.231455 0.216469i
\(276\) 0 0
\(277\) 1502.01i 0.325803i 0.986642 + 0.162901i \(0.0520852\pi\)
−0.986642 + 0.162901i \(0.947915\pi\)
\(278\) 876.896i 0.189182i
\(279\) 0 0
\(280\) −348.344 137.511i −0.0743483 0.0293494i
\(281\) 1443.06 0.306355 0.153178 0.988199i \(-0.451049\pi\)
0.153178 + 0.988199i \(0.451049\pi\)
\(282\) 0 0
\(283\) 4662.08i 0.979264i −0.871929 0.489632i \(-0.837131\pi\)
0.871929 0.489632i \(-0.162869\pi\)
\(284\) −2176.35 −0.454728
\(285\) 0 0
\(286\) 1888.89 0.390532
\(287\) 5997.04i 1.23343i
\(288\) 0 0
\(289\) −3799.21 −0.773297
\(290\) −2912.49 + 7377.95i −0.589750 + 1.49396i
\(291\) 0 0
\(292\) 7098.91i 1.42271i
\(293\) 1105.95i 0.220513i −0.993903 0.110256i \(-0.964833\pi\)
0.993903 0.110256i \(-0.0351672\pi\)
\(294\) 0 0
\(295\) 6402.16 + 2527.29i 1.26355 + 0.498795i
\(296\) 208.136 0.0408705
\(297\) 0 0
\(298\) 904.429i 0.175813i
\(299\) 5691.32 1.10079
\(300\) 0 0
\(301\) 3734.02 0.715035
\(302\) 2019.16i 0.384734i
\(303\) 0 0
\(304\) 4407.92 0.831616
\(305\) 5226.82 + 2063.32i 0.981268 + 0.387361i
\(306\) 0 0
\(307\) 8585.39i 1.59607i −0.602609 0.798036i \(-0.705872\pi\)
0.602609 0.798036i \(-0.294128\pi\)
\(308\) 1329.15i 0.245893i
\(309\) 0 0
\(310\) 4164.55 10549.7i 0.763001 1.93284i
\(311\) 7039.00 1.28342 0.641712 0.766945i \(-0.278224\pi\)
0.641712 + 0.766945i \(0.278224\pi\)
\(312\) 0 0
\(313\) 5196.42i 0.938399i −0.883092 0.469199i \(-0.844543\pi\)
0.883092 0.469199i \(-0.155457\pi\)
\(314\) −8993.89 −1.61642
\(315\) 0 0
\(316\) −1771.12 −0.315295
\(317\) 556.011i 0.0985133i −0.998786 0.0492566i \(-0.984315\pi\)
0.998786 0.0492566i \(-0.0156852\pi\)
\(318\) 0 0
\(319\) 2012.28 0.353185
\(320\) −6110.29 2412.08i −1.06742 0.421372i
\(321\) 0 0
\(322\) 7723.31i 1.33666i
\(323\) 7009.80i 1.20754i
\(324\) 0 0
\(325\) −3422.13 + 3659.04i −0.584080 + 0.624514i
\(326\) −3795.43 −0.644815
\(327\) 0 0
\(328\) 1128.32i 0.189943i
\(329\) 452.011 0.0757452
\(330\) 0 0
\(331\) −509.573 −0.0846184 −0.0423092 0.999105i \(-0.513471\pi\)
−0.0423092 + 0.999105i \(0.513471\pi\)
\(332\) 5570.67i 0.920874i
\(333\) 0 0
\(334\) 7029.22 1.15156
\(335\) −237.092 + 600.603i −0.0386678 + 0.0979536i
\(336\) 0 0
\(337\) 783.515i 0.126649i 0.997993 + 0.0633246i \(0.0201703\pi\)
−0.997993 + 0.0633246i \(0.979830\pi\)
\(338\) 2407.55i 0.387436i
\(339\) 0 0
\(340\) 3301.41 8363.17i 0.526600 1.33399i
\(341\) −2877.34 −0.456940
\(342\) 0 0
\(343\) 6777.76i 1.06695i
\(344\) −702.544 −0.110112
\(345\) 0 0
\(346\) 9994.95 1.55298
\(347\) 630.674i 0.0975688i 0.998809 + 0.0487844i \(0.0155347\pi\)
−0.998809 + 0.0487844i \(0.984465\pi\)
\(348\) 0 0
\(349\) −387.854 −0.0594882 −0.0297441 0.999558i \(-0.509469\pi\)
−0.0297441 + 0.999558i \(0.509469\pi\)
\(350\) −4965.44 4643.95i −0.758325 0.709227i
\(351\) 0 0
\(352\) 2998.34i 0.454012i
\(353\) 2140.74i 0.322776i 0.986891 + 0.161388i \(0.0515971\pi\)
−0.986891 + 0.161388i \(0.948403\pi\)
\(354\) 0 0
\(355\) −2626.87 1036.97i −0.392731 0.155033i
\(356\) 11415.5 1.69950
\(357\) 0 0
\(358\) 4284.42i 0.632510i
\(359\) 1180.69 0.173578 0.0867889 0.996227i \(-0.472339\pi\)
0.0867889 + 0.996227i \(0.472339\pi\)
\(360\) 0 0
\(361\) −1218.95 −0.177716
\(362\) 10855.3i 1.57608i
\(363\) 0 0
\(364\) 4607.59 0.663471
\(365\) −3382.43 + 8568.41i −0.485054 + 1.22874i
\(366\) 0 0
\(367\) 8058.99i 1.14626i −0.819466 0.573128i \(-0.805730\pi\)
0.819466 0.573128i \(-0.194270\pi\)
\(368\) 8334.55i 1.18062i
\(369\) 0 0
\(370\) 3514.54 + 1387.39i 0.493817 + 0.194937i
\(371\) 5648.35 0.790425
\(372\) 0 0
\(373\) 9866.56i 1.36963i 0.728718 + 0.684813i \(0.240116\pi\)
−0.728718 + 0.684813i \(0.759884\pi\)
\(374\) −4398.93 −0.608191
\(375\) 0 0
\(376\) −85.0443 −0.0116644
\(377\) 6975.73i 0.952967i
\(378\) 0 0
\(379\) 4799.17 0.650440 0.325220 0.945638i \(-0.394562\pi\)
0.325220 + 0.945638i \(0.394562\pi\)
\(380\) −6728.96 2656.30i −0.908390 0.358593i
\(381\) 0 0
\(382\) 9063.93i 1.21401i
\(383\) 5701.76i 0.760695i −0.924844 0.380347i \(-0.875804\pi\)
0.924844 0.380347i \(-0.124196\pi\)
\(384\) 0 0
\(385\) −633.301 + 1604.28i −0.0838337 + 0.212368i
\(386\) 19770.6 2.60699
\(387\) 0 0
\(388\) 4857.35i 0.635553i
\(389\) −8912.17 −1.16161 −0.580804 0.814044i \(-0.697262\pi\)
−0.580804 + 0.814044i \(0.697262\pi\)
\(390\) 0 0
\(391\) −13254.2 −1.71431
\(392\) 414.135i 0.0533596i
\(393\) 0 0
\(394\) −1519.06 −0.194237
\(395\) −2137.75 843.889i −0.272308 0.107495i
\(396\) 0 0
\(397\) 9971.00i 1.26053i −0.776381 0.630264i \(-0.782946\pi\)
0.776381 0.630264i \(-0.217054\pi\)
\(398\) 20367.4i 2.56514i
\(399\) 0 0
\(400\) −5358.41 5011.48i −0.669801 0.626435i
\(401\) 710.271 0.0884520 0.0442260 0.999022i \(-0.485918\pi\)
0.0442260 + 0.999022i \(0.485918\pi\)
\(402\) 0 0
\(403\) 9974.54i 1.23292i
\(404\) −2684.62 −0.330606
\(405\) 0 0
\(406\) 9466.30 1.15715
\(407\) 958.563i 0.116743i
\(408\) 0 0
\(409\) −6162.68 −0.745048 −0.372524 0.928023i \(-0.621508\pi\)
−0.372524 + 0.928023i \(0.621508\pi\)
\(410\) 7521.13 19052.6i 0.905957 2.29498i
\(411\) 0 0
\(412\) 702.388i 0.0839907i
\(413\) 8214.30i 0.978691i
\(414\) 0 0
\(415\) 2654.27 6723.81i 0.313959 0.795323i
\(416\) 10394.0 1.22502
\(417\) 0 0
\(418\) 3539.36i 0.414152i
\(419\) −13217.7 −1.54111 −0.770556 0.637372i \(-0.780022\pi\)
−0.770556 + 0.637372i \(0.780022\pi\)
\(420\) 0 0
\(421\) 2760.80 0.319603 0.159802 0.987149i \(-0.448915\pi\)
0.159802 + 0.987149i \(0.448915\pi\)
\(422\) 2296.57i 0.264918i
\(423\) 0 0
\(424\) −1062.72 −0.121722
\(425\) 7969.63 8521.34i 0.909609 0.972578i
\(426\) 0 0
\(427\) 6706.28i 0.760046i
\(428\) 1250.49i 0.141226i
\(429\) 0 0
\(430\) −11863.0 4682.99i −1.33043 0.525195i
\(431\) 3057.57 0.341712 0.170856 0.985296i \(-0.445347\pi\)
0.170856 + 0.985296i \(0.445347\pi\)
\(432\) 0 0
\(433\) 14533.5i 1.61302i 0.591221 + 0.806510i \(0.298646\pi\)
−0.591221 + 0.806510i \(0.701354\pi\)
\(434\) −13535.8 −1.49709
\(435\) 0 0
\(436\) 2812.94 0.308980
\(437\) 10664.3i 1.16737i
\(438\) 0 0
\(439\) 1497.89 0.162848 0.0814240 0.996680i \(-0.474053\pi\)
0.0814240 + 0.996680i \(0.474053\pi\)
\(440\) 119.153 301.841i 0.0129100 0.0327038i
\(441\) 0 0
\(442\) 15249.3i 1.64103i
\(443\) 13363.3i 1.43320i 0.697484 + 0.716600i \(0.254303\pi\)
−0.697484 + 0.716600i \(0.745697\pi\)
\(444\) 0 0
\(445\) 13778.6 + 5439.19i 1.46779 + 0.579421i
\(446\) −21907.2 −2.32587
\(447\) 0 0
\(448\) 7839.83i 0.826779i
\(449\) −15023.0 −1.57902 −0.789509 0.613739i \(-0.789665\pi\)
−0.789509 + 0.613739i \(0.789665\pi\)
\(450\) 0 0
\(451\) −5196.45 −0.542553
\(452\) 448.207i 0.0466414i
\(453\) 0 0
\(454\) 4531.44 0.468439
\(455\) 5561.38 + 2195.39i 0.573015 + 0.226201i
\(456\) 0 0
\(457\) 14460.7i 1.48018i −0.672507 0.740091i \(-0.734782\pi\)
0.672507 0.740091i \(-0.265218\pi\)
\(458\) 8306.38i 0.847449i
\(459\) 0 0
\(460\) 5022.56 12723.2i 0.509083 1.28961i
\(461\) 6397.52 0.646339 0.323170 0.946341i \(-0.395252\pi\)
0.323170 + 0.946341i \(0.395252\pi\)
\(462\) 0 0
\(463\) 6228.94i 0.625234i 0.949879 + 0.312617i \(0.101206\pi\)
−0.949879 + 0.312617i \(0.898794\pi\)
\(464\) 10215.5 1.02207
\(465\) 0 0
\(466\) 8670.51 0.861917
\(467\) 1434.12i 0.142105i 0.997473 + 0.0710526i \(0.0226358\pi\)
−0.997473 + 0.0710526i \(0.977364\pi\)
\(468\) 0 0
\(469\) 770.605 0.0758705
\(470\) −1436.04 566.885i −0.140935 0.0556350i
\(471\) 0 0
\(472\) 1545.49i 0.150714i
\(473\) 3235.54i 0.314525i
\(474\) 0 0
\(475\) −6856.23 6412.32i −0.662285 0.619405i
\(476\) −10730.4 −1.03325
\(477\) 0 0
\(478\) 8082.71i 0.773419i
\(479\) −12095.5 −1.15378 −0.576888 0.816823i \(-0.695733\pi\)
−0.576888 + 0.816823i \(0.695733\pi\)
\(480\) 0 0
\(481\) −3322.94 −0.314996
\(482\) 17200.5i 1.62544i
\(483\) 0 0
\(484\) 10316.0 0.968822
\(485\) −2314.39 + 5862.84i −0.216683 + 0.548903i
\(486\) 0 0
\(487\) 9600.57i 0.893313i −0.894706 0.446656i \(-0.852615\pi\)
0.894706 0.446656i \(-0.147385\pi\)
\(488\) 1261.76i 0.117044i
\(489\) 0 0
\(490\) 2760.52 6992.98i 0.254505 0.644716i
\(491\) 2091.41 0.192228 0.0961141 0.995370i \(-0.469359\pi\)
0.0961141 + 0.995370i \(0.469359\pi\)
\(492\) 0 0
\(493\) 16245.4i 1.48409i
\(494\) 12269.5 1.11747
\(495\) 0 0
\(496\) −14607.0 −1.32233
\(497\) 3370.41i 0.304192i
\(498\) 0 0
\(499\) 18595.9 1.66827 0.834133 0.551563i \(-0.185968\pi\)
0.834133 + 0.551563i \(0.185968\pi\)
\(500\) 5159.93 + 10879.4i 0.461518 + 0.973085i
\(501\) 0 0
\(502\) 6679.27i 0.593845i
\(503\) 5038.79i 0.446657i −0.974743 0.223329i \(-0.928308\pi\)
0.974743 0.223329i \(-0.0716923\pi\)
\(504\) 0 0
\(505\) −3240.35 1279.15i −0.285532 0.112716i
\(506\) −6692.26 −0.587959
\(507\) 0 0
\(508\) 2291.89i 0.200170i
\(509\) 6501.99 0.566200 0.283100 0.959090i \(-0.408637\pi\)
0.283100 + 0.959090i \(0.408637\pi\)
\(510\) 0 0
\(511\) 10993.7 0.951729
\(512\) 16400.1i 1.41560i
\(513\) 0 0
\(514\) −25139.6 −2.15731
\(515\) −334.668 + 847.785i −0.0286354 + 0.0725395i
\(516\) 0 0
\(517\) 391.668i 0.0333183i
\(518\) 4509.34i 0.382488i
\(519\) 0 0
\(520\) −1046.36 413.055i −0.0882418 0.0348340i
\(521\) 3689.43 0.310244 0.155122 0.987895i \(-0.450423\pi\)
0.155122 + 0.987895i \(0.450423\pi\)
\(522\) 0 0
\(523\) 5040.68i 0.421441i −0.977546 0.210720i \(-0.932419\pi\)
0.977546 0.210720i \(-0.0675810\pi\)
\(524\) 21904.9 1.82619
\(525\) 0 0
\(526\) −25932.7 −2.14965
\(527\) 23229.2i 1.92007i
\(528\) 0 0
\(529\) −7997.15 −0.657282
\(530\) −17944.8 7083.82i −1.47070 0.580569i
\(531\) 0 0
\(532\) 8633.61i 0.703599i
\(533\) 18013.9i 1.46392i
\(534\) 0 0
\(535\) −595.823 + 1509.34i −0.0481489 + 0.121971i
\(536\) −144.987 −0.0116837
\(537\) 0 0
\(538\) 9802.75i 0.785552i
\(539\) −1907.28 −0.152416
\(540\) 0 0
\(541\) 744.536 0.0591684 0.0295842 0.999562i \(-0.490582\pi\)
0.0295842 + 0.999562i \(0.490582\pi\)
\(542\) 28478.6i 2.25694i
\(543\) 0 0
\(544\) −24206.1 −1.90777
\(545\) 3395.23 + 1340.29i 0.266855 + 0.105342i
\(546\) 0 0
\(547\) 6401.69i 0.500396i −0.968195 0.250198i \(-0.919504\pi\)
0.968195 0.250198i \(-0.0804957\pi\)
\(548\) 1064.02i 0.0829428i
\(549\) 0 0
\(550\) 4023.99 4302.56i 0.311970 0.333567i
\(551\) 13071.0 1.01060
\(552\) 0 0
\(553\) 2742.84i 0.210918i
\(554\) −6122.60 −0.469538
\(555\) 0 0
\(556\) 1853.47 0.141375
\(557\) 6623.77i 0.503874i 0.967744 + 0.251937i \(0.0810676\pi\)
−0.967744 + 0.251937i \(0.918932\pi\)
\(558\) 0 0
\(559\) 11216.3 0.848653
\(560\) −3215.00 + 8144.26i −0.242604 + 0.614567i
\(561\) 0 0
\(562\) 5882.29i 0.441512i
\(563\) 13355.7i 0.999778i 0.866089 + 0.499889i \(0.166626\pi\)
−0.866089 + 0.499889i \(0.833374\pi\)
\(564\) 0 0
\(565\) 213.558 540.988i 0.0159017 0.0402824i
\(566\) 19003.8 1.41129
\(567\) 0 0
\(568\) 634.131i 0.0468443i
\(569\) −20926.1 −1.54177 −0.770887 0.636972i \(-0.780187\pi\)
−0.770887 + 0.636972i \(0.780187\pi\)
\(570\) 0 0
\(571\) 25369.8 1.85936 0.929679 0.368370i \(-0.120084\pi\)
0.929679 + 0.368370i \(0.120084\pi\)
\(572\) 3992.49i 0.291843i
\(573\) 0 0
\(574\) −24445.5 −1.77759
\(575\) 12124.5 12963.8i 0.879351 0.940226i
\(576\) 0 0
\(577\) 2474.30i 0.178521i −0.996008 0.0892605i \(-0.971550\pi\)
0.996008 0.0892605i \(-0.0284504\pi\)
\(578\) 15486.6i 1.11446i
\(579\) 0 0
\(580\) −15594.6 6156.05i −1.11643 0.440717i
\(581\) −8627.01 −0.616022
\(582\) 0 0
\(583\) 4894.30i 0.347687i
\(584\) −2068.43 −0.146562
\(585\) 0 0
\(586\) 4508.13 0.317797
\(587\) 15752.6i 1.10763i −0.832639 0.553817i \(-0.813171\pi\)
0.832639 0.553817i \(-0.186829\pi\)
\(588\) 0 0
\(589\) −18690.1 −1.30749
\(590\) −10301.9 + 26096.8i −0.718850 + 1.82100i
\(591\) 0 0
\(592\) 4866.22i 0.337838i
\(593\) 6162.03i 0.426719i 0.976974 + 0.213360i \(0.0684406\pi\)
−0.976974 + 0.213360i \(0.931559\pi\)
\(594\) 0 0
\(595\) −12951.6 5112.73i −0.892377 0.352271i
\(596\) 1911.67 0.131384
\(597\) 0 0
\(598\) 23199.3i 1.58644i
\(599\) 7814.07 0.533012 0.266506 0.963833i \(-0.414131\pi\)
0.266506 + 0.963833i \(0.414131\pi\)
\(600\) 0 0
\(601\) −24315.4 −1.65033 −0.825164 0.564893i \(-0.808917\pi\)
−0.825164 + 0.564893i \(0.808917\pi\)
\(602\) 15220.8i 1.03049i
\(603\) 0 0
\(604\) −4267.85 −0.287510
\(605\) 12451.5 + 4915.29i 0.836734 + 0.330306i
\(606\) 0 0
\(607\) 1586.65i 0.106096i −0.998592 0.0530478i \(-0.983106\pi\)
0.998592 0.0530478i \(-0.0168936\pi\)
\(608\) 19476.1i 1.29911i
\(609\) 0 0
\(610\) −8410.61 + 21305.8i −0.558255 + 1.41418i
\(611\) 1357.75 0.0898997
\(612\) 0 0
\(613\) 12856.4i 0.847089i 0.905875 + 0.423545i \(0.139214\pi\)
−0.905875 + 0.423545i \(0.860786\pi\)
\(614\) 34996.3 2.30022
\(615\) 0 0
\(616\) −387.277 −0.0253309
\(617\) 3854.46i 0.251499i 0.992062 + 0.125749i \(0.0401335\pi\)
−0.992062 + 0.125749i \(0.959867\pi\)
\(618\) 0 0
\(619\) −5644.03 −0.366482 −0.183241 0.983068i \(-0.558659\pi\)
−0.183241 + 0.983068i \(0.558659\pi\)
\(620\) 22298.5 + 8802.48i 1.44440 + 0.570187i
\(621\) 0 0
\(622\) 28692.8i 1.84964i
\(623\) 17678.7i 1.13689i
\(624\) 0 0
\(625\) 1044.31 + 15590.1i 0.0668360 + 0.997764i
\(626\) 21181.9 1.35240
\(627\) 0 0
\(628\) 19010.1i 1.20794i
\(629\) 7738.62 0.490555
\(630\) 0 0
\(631\) −6379.75 −0.402494 −0.201247 0.979541i \(-0.564499\pi\)
−0.201247 + 0.979541i \(0.564499\pi\)
\(632\) 516.057i 0.0324804i
\(633\) 0 0
\(634\) 2266.44 0.141975
\(635\) −1092.02 + 2766.32i −0.0682451 + 0.172879i
\(636\) 0 0
\(637\) 6611.75i 0.411251i
\(638\) 8202.57i 0.509001i
\(639\) 0 0
\(640\) 1315.24 3331.79i 0.0812337 0.205782i
\(641\) −19543.9 −1.20427 −0.602135 0.798395i \(-0.705683\pi\)
−0.602135 + 0.798395i \(0.705683\pi\)
\(642\) 0 0
\(643\) 26175.3i 1.60537i −0.596401 0.802686i \(-0.703403\pi\)
0.596401 0.802686i \(-0.296597\pi\)
\(644\) −16324.5 −0.998877
\(645\) 0 0
\(646\) −28573.7 −1.74028
\(647\) 20349.8i 1.23653i −0.785971 0.618264i \(-0.787836\pi\)
0.785971 0.618264i \(-0.212164\pi\)
\(648\) 0 0
\(649\) 7117.71 0.430500
\(650\) −14915.2 13949.5i −0.900033 0.841761i
\(651\) 0 0
\(652\) 8022.30i 0.481867i
\(653\) 21661.4i 1.29813i −0.760734 0.649064i \(-0.775161\pi\)
0.760734 0.649064i \(-0.224839\pi\)
\(654\) 0 0
\(655\) 26439.3 + 10437.1i 1.57721 + 0.622612i
\(656\) −26380.2 −1.57008
\(657\) 0 0
\(658\) 1842.51i 0.109162i
\(659\) 9447.97 0.558484 0.279242 0.960221i \(-0.409917\pi\)
0.279242 + 0.960221i \(0.409917\pi\)
\(660\) 0 0
\(661\) −14301.8 −0.841569 −0.420784 0.907161i \(-0.638245\pi\)
−0.420784 + 0.907161i \(0.638245\pi\)
\(662\) 2077.15i 0.121950i
\(663\) 0 0
\(664\) 1623.14 0.0948647
\(665\) −4113.67 + 10420.8i −0.239882 + 0.607671i
\(666\) 0 0
\(667\) 24714.8i 1.43472i
\(668\) 14857.5i 0.860558i
\(669\) 0 0
\(670\) −2448.21 966.447i −0.141168 0.0557270i
\(671\) 5811.00 0.334324
\(672\) 0 0
\(673\) 13078.6i 0.749096i −0.927208 0.374548i \(-0.877798\pi\)
0.927208 0.374548i \(-0.122202\pi\)
\(674\) −3193.81 −0.182524
\(675\) 0 0
\(676\) −5088.77 −0.289529
\(677\) 15622.6i 0.886891i 0.896301 + 0.443446i \(0.146244\pi\)
−0.896301 + 0.443446i \(0.853756\pi\)
\(678\) 0 0
\(679\) 7522.33 0.425156
\(680\) 2436.80 + 961.942i 0.137422 + 0.0542483i
\(681\) 0 0
\(682\) 11728.8i 0.658531i
\(683\) 3176.18i 0.177940i −0.996034 0.0889701i \(-0.971642\pi\)
0.996034 0.0889701i \(-0.0283576\pi\)
\(684\) 0 0
\(685\) −506.975 + 1284.27i −0.0282781 + 0.0716345i
\(686\) −27627.9 −1.53766
\(687\) 0 0
\(688\) 16425.4i 0.910195i
\(689\) 16966.5 0.938132
\(690\) 0 0
\(691\) 30731.4 1.69186 0.845931 0.533293i \(-0.179046\pi\)
0.845931 + 0.533293i \(0.179046\pi\)
\(692\) 21126.0i 1.16054i
\(693\) 0 0
\(694\) −2570.79 −0.140614
\(695\) 2237.14 + 883.126i 0.122100 + 0.0481998i
\(696\) 0 0
\(697\) 41951.7i 2.27982i
\(698\) 1580.99i 0.0857328i
\(699\) 0 0
\(700\) 9815.78 10495.3i 0.530003 0.566693i
\(701\) −18536.2 −0.998718 −0.499359 0.866395i \(-0.666431\pi\)
−0.499359 + 0.866395i \(0.666431\pi\)
\(702\) 0 0
\(703\) 6226.45i 0.334047i
\(704\) −6793.22 −0.363678
\(705\) 0 0
\(706\) −8726.19 −0.465176
\(707\) 4157.54i 0.221160i
\(708\) 0 0
\(709\) 16619.3 0.880325 0.440162 0.897918i \(-0.354921\pi\)
0.440162 + 0.897918i \(0.354921\pi\)
\(710\) 4226.96 10707.8i 0.223430 0.565994i
\(711\) 0 0
\(712\) 3326.18i 0.175076i
\(713\) 35339.4i 1.85620i
\(714\) 0 0
\(715\) −1902.31 + 4818.95i −0.0994997 + 0.252054i
\(716\) 9055.86 0.472672
\(717\) 0 0
\(718\) 4812.80i 0.250156i
\(719\) 10245.8 0.531441 0.265720 0.964050i \(-0.414390\pi\)
0.265720 + 0.964050i \(0.414390\pi\)
\(720\) 0 0
\(721\) 1087.75 0.0561859
\(722\) 4968.77i 0.256120i
\(723\) 0 0
\(724\) 22944.6 1.17780
\(725\) −15889.5 14860.8i −0.813961 0.761261i
\(726\) 0 0
\(727\) 30936.5i 1.57823i −0.614247 0.789114i \(-0.710540\pi\)
0.614247 0.789114i \(-0.289460\pi\)
\(728\) 1342.53i 0.0683481i
\(729\) 0 0
\(730\) −34927.0 13787.7i −1.77083 0.699047i
\(731\) −26121.0 −1.32164
\(732\) 0 0
\(733\) 3336.77i 0.168140i 0.996460 + 0.0840698i \(0.0267919\pi\)
−0.996460 + 0.0840698i \(0.973208\pi\)
\(734\) 32850.5 1.65195
\(735\) 0 0
\(736\) −36825.6 −1.84431
\(737\) 667.731i 0.0333734i
\(738\) 0 0
\(739\) 23494.6 1.16950 0.584752 0.811212i \(-0.301192\pi\)
0.584752 + 0.811212i \(0.301192\pi\)
\(740\) −2932.48 + 7428.58i −0.145676 + 0.369027i
\(741\) 0 0
\(742\) 23024.1i 1.13914i
\(743\) 2905.75i 0.143475i 0.997424 + 0.0717373i \(0.0228543\pi\)
−0.997424 + 0.0717373i \(0.977146\pi\)
\(744\) 0 0
\(745\) 2307.39 + 910.856i 0.113471 + 0.0447935i
\(746\) −40218.6 −1.97387
\(747\) 0 0
\(748\) 9297.89i 0.454498i
\(749\) 1936.57 0.0944735
\(750\) 0 0
\(751\) 30691.2 1.49126 0.745632 0.666358i \(-0.232148\pi\)
0.745632 + 0.666358i \(0.232148\pi\)
\(752\) 1988.33i 0.0964189i
\(753\) 0 0
\(754\) 28434.9 1.37339
\(755\) −5151.31 2033.51i −0.248312 0.0980226i
\(756\) 0 0
\(757\) 35875.7i 1.72249i −0.508192 0.861244i \(-0.669686\pi\)
0.508192 0.861244i \(-0.330314\pi\)
\(758\) 19562.6i 0.937397i
\(759\) 0 0
\(760\) 773.974 1960.64i 0.0369408 0.0935787i
\(761\) −26842.1 −1.27861 −0.639307 0.768951i \(-0.720779\pi\)
−0.639307 + 0.768951i \(0.720779\pi\)
\(762\) 0 0
\(763\) 4356.26i 0.206694i
\(764\) 19158.2 0.907223
\(765\) 0 0
\(766\) 23241.8 1.09629
\(767\) 24674.1i 1.16158i
\(768\) 0 0
\(769\) −12755.2 −0.598133 −0.299067 0.954232i \(-0.596675\pi\)
−0.299067 + 0.954232i \(0.596675\pi\)
\(770\) −6539.47 2581.50i −0.306060 0.120819i
\(771\) 0 0
\(772\) 41788.6i 1.94819i
\(773\) 9984.62i 0.464582i −0.972646 0.232291i \(-0.925378\pi\)
0.972646 0.232291i \(-0.0746222\pi\)
\(774\) 0 0
\(775\) 22720.3 + 21249.3i 1.05308 + 0.984898i
\(776\) −1415.30 −0.0654721
\(777\) 0 0
\(778\) 36328.3i 1.67408i
\(779\) −33754.1 −1.55246
\(780\) 0 0
\(781\) −2920.46 −0.133806
\(782\) 54027.6i 2.47062i
\(783\) 0 0
\(784\) −9682.45 −0.441074
\(785\) 9057.80 22945.3i 0.411830 1.04325i
\(786\) 0 0
\(787\) 35676.2i 1.61591i 0.589245 + 0.807954i \(0.299425\pi\)
−0.589245 + 0.807954i \(0.700575\pi\)
\(788\) 3210.80i 0.145152i
\(789\) 0 0
\(790\) 3439.91 8714.01i 0.154920 0.392444i
\(791\) −694.116 −0.0312009
\(792\) 0 0
\(793\) 20144.3i 0.902076i
\(794\) 40644.3 1.81664